I think so, if say the equation it's modeling is very sensitive to input parameters. If a change in a varible of say one part in a billion causes a large change in output, then the equation is chaotic, but every time you input the EXACT same input as a previous time, you will get the same anwser, so it is deterministic too.
Any random data generated by a computer is known as pseudorandom, data that has the characteristics of random data but that was created (and can be exactly recreated by) an algorithm.
The computer could sample information from the environment (CPU temperature or fan speed would be fairly easy to get) and that would be truly random. For it to be useable you’d probably need to process it a bit first though.
I've changed my mind, I agree with MisterBig, it's impossible for a computer to have random output without random input. True randomness is impossible to recreate. I don't know how I explicitly stated that a computer will come up with the same anwser in a "chaotic" equation if the inputs are EXACTLY the same without seeing the flaw in my logic.
One complication here is the use of the word "Chaos".
The mathematical theory of chaos (taking it's name from Yorke's paper "Period Three Implies Chaos") is deterministic, not random.
In a sense it's the opposite of the "Central Limit Theorem".
We've all seen the demonstration where if you drop a large number of marbles (or shot) onto a grid so that each one goes left or right a number of times and then the "pile" comes right up to a pre-drawn curve. In other words, a sequence of purely random events can give a pre-determined result.
"Chaos" (again, technical, mathematical meaning) refers to a purely deterministic process that is so sensitive to "initial conditions" that it is impossible to predict the results.
Simple example: given x_{n}, double it. If the result is larger than 1, drop the integer part: x_{n+1}= (2 x_{n}) modulo 1.
One can show that two intial values arbitrarily close together can rapidly give completely unrelated values.
Any basic inquiry into what chaos theory is would teach you that, as HallsOfIvy pointed out, chaos is entirely a study of deterministic systems. It has nothing to do with "true randomness," which is an entirely different topic.
Actually, it wouldn't hurt to define 'chaos' or 'randomness'. I personally don't think 'true randomness' is possible unless acausal is involved, in principle.
Of course computer can create chaos. See http://www.isp.nwu.edu/~rocky/Pendulum/QuintuplePendulum.html [Broken]
It can compute trajectory that is chaotic. But there's no way to determine what caused it given trajectory alone.
How do you define 'randomness'? There are many definitions. For eg. infinite period before repitition begins. Its enough to calculate Pi infinitely to produce randomness. For eg. maximum information density. Then generate white noise.
Most people in the "biz" call chaos theory, "Nonlinear Dynamics" these days. It's a little more accurate and doesn't have the who baggage where people think chaos = random.
They actually manufacture electronic noise generator circuits that you can hook up to a computer to generate random bit patterns, so that you will have true random input. Not a very common piece of computer hardware though.
The discrete nature of an electronic digital computer precludes in general its representing instantaneous chaos. A quantum computer, being linear, cannot fully reproduce fractal patterns. Careless superfast computer architecture can induce, on small-scale, nonlinear resonances analogous to those on the grid of the Great Blackout in 1960's New York.
of course a computer can generate chaos, I remebr well in my first year of university that we inpute chaotic algorithms into the computers in the lab to model chaotic systems.
Modern day computers cannot generate true randomness, though I beleivethere is a device (maybe it's still in the developmental stage) which uses the probabiltistic nature of QM to generate truly random numbers,
When you seek for true randomness in computers, you need to ask if what you mean is randomness generated by computer alone, or with help of external environment. Thats crucial distinction, as for practical purposes, 'true' randomness is needed and taken from environment. But computer alone cannot generate 'true' randomness.
To get truely random numbers, many comps are using human keyboard input as initial conditions in chaotic algoritm. Like every time you type something, comp measures time between keystrokes and randomness depends on that heavily. Thats about simplest way to get randomness form environment.
In addition, thermal conditions affect frequency of operation abit, and if computer has 2 independant clocks, minute differences between them are dependant on environment alone. The only task is to amplify these tiny changes by chaotic algoritm into randomness.
The answer to the question, can computers create random numbers? Of course depends on the inputs to create the numbers. If no input(ie a pseudo random number generator) then no*. If the input is random then yes. Intel therefore have created the Intel Random Number Generator on their chips to create what should be truly random numbers.
http://apps.intel.com/scripts-util/download.asp?url=/design/security/rng/techbrief.pdf&title=The+Intel+Random+Number+Generator&fullpg=3&site=Developer [Broken]
Very useful if you are encrypting data.
Some encryption products like PGP get inputs from keyboard and mouse use. These provide non-deterministic input to help create random numbers.
Duncan
* If you define random numbers as being non-deterministic.
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